Question

From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8 cm and base radius 6 cm is hollowed out. Find the volume of the remaining solid. Also, find the total surface area of the remaining solid.

Answer 1

Volume of the solid left = Volume of cylinder - Volume of cone `=pir^2h - 1/3pir^2h = 2/3 xx 22/7 xx 8 xx 6 xx 6 = 603.428   "cm^3'` 

The slant length of the cone , `l =sqrt(r^2 + h^2) = sqrt(36+64) = 10 "cm"`

Total surface area of final solid = Area of base circle 

Answer 2

Volume of the solid left = Volume of cylinder - Volume of cone `=pir^2h - 1/3pir^2h = 2/3 xx 22/7 xx 8 xx 6 xx 6 = 603.428   "cm^3'` 

The slant length of the cone ,`l =sqrt(r^2 + h^2) = sqrt(36+64) = 10 "cm"` 

Total surface area of final solid = Area of base circle + Curved surface area of cylinder +curved area of once`= pirl^2 + 2pirh + pirl = pir (r + 2h +l) = 22/7 xx 6 xx (6 + 16 + 10) = 603.42  "cm"^2`